Assuming the win was achieved not merely with different engineering choices but with greater spending, and considering the relative economic inefficiency of the Soviet system, it may have hastened the USSRs collapse - I imagine along the same lines of 1989-91, but not more dangerously than that.
Reducing everything to economics is the greatest disease of our times. If our ancestors followed economics, they would be still sitting on trees. After all, what sense does it make to go down to the ground and face all these predators, when trees offer relative safety?
In human society, there are forces stronger than economics. Vision. Inspiration. Values. Collective dreams. If one can plant ideas in people's minds, what kind of power does he have? Enormous. That's the power that transcends political and cultural boundaries, the power which dwarfs economic or military might. Perhaps the best popular explanation of the concept is in the movie
Inception:
Dom Cobb: Mr. Saito, this...this isn't your typical corporate espionage. You...you asked me for inception, I do hope you understand the gravity of that request. The seed that we plant in this man's mind will grow into an idea. This idea will define him. It may come to change...well, it may come to change everything about him.
Dom Cobb: "I will split up my father's empire." Now this is obviously an idea that Robert himself will choose to reject. Which is why we need to plant it deep in his subconscious. Subconscious is motivated by emotion, right? Not reason. We need to find a way to translate this into an emotional concept.
Arthur: How do you translate a business stratedgy into an emotion?
What, then, do you need to plant ideas into people's mind?
Images.
Apollo produced three images which entered collective subconcious.
The first one was the
Earthrise photo from Apollo 8. That image, together with
The Blue Marble from Apollo 17 became the catalyst of the environmetal movement. The most unexpected result of the whole endeavour, probably. The third image was, of course, AS11-40-5874 -- Buzz Aldrin standing next to the US flag on the Moon. The most expensive photo in the whole history of propaganda. Yet also one of the most powerful.
The world's kids (Soviet kids included) saw an American flag on the Moon. The Americans have touched the Moon, and so, even the sky was no longer a limit for them. This was instrumental in instilling the idea that the American system is better than the Soviet system in the collective subconcious of the humanity.
After some 20 years, the idea became even acceped by the Soviet leaders, who dissolved the Union and embraced capitalism. Ironically, this has caused their country to enter a deep crisis, which dwarfed the economic problems of 1980.
And so, the OP's question cannot be merely analyzed on political grounds. You must think what ideas would be
incepted into human minds by different images.
If the world had seen a Soviet flag on the Moon, would the world instead accept superiority of the Soviet system and started moving to a more collective social and economic model?
If people had seen a Soviet and an American shaking hands on the Moon, would they opt to choose cooperation over the insanity of arms race?
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